The structure of the $$v_2$$-local algebraic $$\text {tmf}$$ resolution

Abstract We give a complete description of the $$E_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> -term of the $$v_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>v</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -local as well as g -local algebraic $$\text {tmf}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>tmf</mml:mtext> </mml:math> resolution.